$A$ uniform rod of mass $m$,length $L$,area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be

$A$ rod of length $l$ and area of cross-section $A$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The rod is so placed that it is not allowed to increase in length,then the force developed is proportional to

Which coefficient of elasticity is responsible for the propagation of a wave in a string?

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

The ratio of the lengths of two wires $A$ and $B$ of the same material is $1 : 2$ and the ratio of their diameters is $2 : 1$. If they are stretched by the same force,what is the ratio of the increase in their lengths?

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)